Average Error: 5.7 → 3.0
Time: 1.6s
Precision: 64
\[\frac{x \cdot y}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.0564275001021605 \cdot 10^{274}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \le 4.3742218092142276 \cdot 10^{124}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]
\frac{x \cdot y}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le -3.0564275001021605 \cdot 10^{274}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;x \cdot y \le 4.3742218092142276 \cdot 10^{124}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\end{array}
double code(double x, double y, double z) {
	return ((x * y) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x * y) <= -3.0564275001021605e+274)) {
		VAR = (1.0 / ((z / x) / y));
	} else {
		double VAR_1;
		if (((x * y) <= 4.374221809214228e+124)) {
			VAR_1 = ((x * y) / z);
		} else {
			VAR_1 = (x / (z / y));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target6.3
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -4.262230790519429 \cdot 10^{-138}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \lt 1.70421306606504721 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -3.0564275001021605e+274

    1. Initial program 44.6

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied clear-num44.6

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.6

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]

    if -3.0564275001021605e+274 < (* x y) < 4.374221809214228e+124

    1. Initial program 3.0

      \[\frac{x \cdot y}{z}\]

    if 4.374221809214228e+124 < (* x y)

    1. Initial program 16.6

      \[\frac{x \cdot y}{z}\]
    2. Using strategy rm

    3. Applied associate-/l*3.9

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le -3.0564275001021605 \cdot 10^{274}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;x \cdot y \le 4.3742218092142276 \cdot 10^{124}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< z -4.262230790519429e-138) (/ (* x y) z) (if (< z 1.7042130660650472e-164) (/ x (/ z y)) (* (/ x z) y)))

  (/ (* x y) z))